Školjka

%V0 Determine the lowest possible value of the expression $$ \frac{1}{a + x} + \frac{1}{a + y} + \frac{1}{b + x} + \frac{1}{b + y} \text{,} $$ where $a$, $b$, $x$, and $y$ are positive real numbers satisfying the inequalities $$ \frac{1}{a + x} \geq \frac12, \quad \frac{1}{a + y} \geq \frac12, \quad \frac{1}{b + x} \geq \frac12, \quad \text{and} \ \frac{1}{b + y} \geq 1 \text{.} $$